Question: Rewrite as a simplified fraction. ${0.4\overline{5} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 45.5555...\\ 10x &= 4.5555...\end{align*}}$ Subtracting the two equations, we have: ${90x = 41}$ ${x = \dfrac{41}{90}} $